Question: Simplify to lowest terms. $\dfrac{54}{90}$
Answer: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 54 and 90? $54 = 2\cdot3\cdot3\cdot3$ $90 = 2\cdot3\cdot3\cdot5$ $\mbox{GCD}(54, 90) = 2\cdot3\cdot3 = 18$ $\dfrac{54}{90} = \dfrac{3 \cdot 18}{ 5\cdot 18}$ $\hphantom{\dfrac{54}{90}} = \dfrac{3}{5} \cdot \dfrac{18}{18}$ $\hphantom{\dfrac{54}{90}} = \dfrac{3}{5} \cdot 1$ $\hphantom{\dfrac{54}{90}} = \dfrac{3}{5}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{54}{90}= \dfrac{2\cdot27}{2\cdot45}= \dfrac{2\cdot 3\cdot9}{2\cdot 3\cdot15}= \dfrac{2\cdot 3\cdot 3\cdot3}{2\cdot 3\cdot 3\cdot5}= \dfrac{3}{5}$